Question

A Euglena culture is measured at 1.6 x 10³ cells/ml at 12:00 noon on Tuesday, and by 6:00 pm on Friday it has increased to 9.3 x 10³ cells/ml. What is the rate constant "k" for this culture, expressed in the proper units?

Answer 1

Number of generations per hour is rate constant.

No = Initial count of bacteria = 1.6 × 10^3 cells per mL

Nt = Final count of bacteria = 9.3 × 10^3 cells per mL

t = Total time = 78 hours (from tuesday to friday)

Nt = No 2^n

n is the # of generations

9.3 × 10^3 = (1.6 × 10^3) 2^n

2^n = 5.81

n log 2 = log 5.81

n = 0.764 / 0.301 = 2.53

Approximately 2.5 generations in 78 hours.

So, # generations in one hour = 2.5 / 78 = 0.03205

k = 0.03205 (answer)

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